1. Find the antiderivative of each of the following functions. 3 a. f(x) =+ e* + Vx b. f(x) = sin (5x) + cos (4x) c. f(x) = 9. - e3x

Q: 1. Find the derivative of the following functions: a. y = x² b. y=x4 c. y=- X

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Q: 5. Evaluate (x) dx for the following functions: 1 (a) f(x) = Vx + (b) f(x) = e2x %3D (c) f(x) =…

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Q: 3 - 1 Find the derivative of y = - 3 with respect tox. tan A. 3 x +9 В. + 9 С. 1 x +9 D. x² +9 B.

A: Use given function find derivative

Q: 5. Find the second derivative of the function. Simplify. f(x) = sin(x) 1+ cos(x)

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Q: find the cosine of the angle between the vectors. 3i + k, i + j + k

A: Let,u = 3i+kv = i+j+kFormula for finding the cosine of the angle between two vectors is given by -…

Q: 6. Let sin x g(x) = [ Find g (7) 3 3 + -dt

A: Given; g(x)= integraion of sqrt[3/(1/4 +t2)], limit from 1 to sinx.

Q: 10. Use the chain rule and the fundamental theorem of calculus to compute the derivative of the…

A: Liebniz rule for differentiation under integral sign:Let…

Q: Calculate L4 for f(x) = 36 cos (2) over L4 = - over [27,27]. 4

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Q: Activity 4: Let F be functions defined by the following. Find their derivatives then list down three…

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